363 IGPM363.pdf        April 2013
TITLE Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations
AUTHORS Markus Bachmayr, Wolfgang Dahmen
ABSTRACT We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous convergence analysis, where all parameters required for the execution of the methods depend only on the underlying infinite-dimensional problem, but not on a concrete discretization. Under certain assumptions on the rates for the involved low-rank approximations and basis expansions, we can also give bounds on the computational complexity of the iteration as a function of the prescribed target error. Our theoretical findings are illustrated and supported by computational experiments. These demonstrate that problems in very high dimensions can be treated with controlled solution accuracy.
KEYWORDS low-rank tensor approximation, adaptive methods, high-dimensional operator equations, computational complexity
DOI 10.1007/S10208-013-9187-3
PUBLICATION Foundations of Computational Mathematics
15(2015), 839-898

Oberwolfach reports : OWR 10(3), 2179-2257 (2013)
DOI: 10.4171/OWR/2013/39